136 THE INTERFEROMETRY OF 



if, for brevity, t'-t = St and AN-AN' = dN; or 



If is not quite equal to p', $(p' p) may still be neglected, but bN/p and 

 &N'/p' must replace AN and AA/"', orAN(i 8p/p) replace AJV where 8p = 

 p-p'. 



On applying equation (5) to series i, 2, 3, for which p is nearly constant, 



= 0.00423 01 = 0.00380 



applying it to series 4, 5, 7, similarly, 



52 = 79.8 SJV = 0.00404 01 = 0.00404 



The mean value is thus 01 = 0.00392. The reason of this difference is found in 

 series 4, where AAT is excessive. In fact, if we compare percentage errors of 

 a and SN 



so that an error of 5 per cent in 8N would be an error of over 5 per cent in a. 

 For the case where the fringes tremble this is inevitable. If the mounting were 

 without tremor, however, dN should be guaranteed to sXio- 5 cm., corre- 

 sponding to the evanescence of a single interference ring, so that a should be 

 determinable to i per cent, even in case of a tube of the length 71.7 cm. given. 

 If *>t is small or t' small, equation (5) becomes, approximately, 



= at or 



This equation may be used to find the successive values of AAf in the table, 

 if the second, for instance, is supposed to be correct. It appears that the 

 first and fifth differ about equally ( = 0.0001 cm.) from the second, but the 

 error of the fourth ( 0.00028) is excessive. Hence if this second datum be 

 taken as the mean of series i, 2, 5, and combined with the two data for 100, 



AAT = 19.28 5AT = o.42i 6^ = 78. 6 *'= 100.3 = 0.00385 



This is the more probable result of table 14 and would agree with Mascart's 

 value, 0.00382. 



Somewhat later, the independent series of observations 6 and 8 were carried 

 out. The interference pattern at 99.7 was exceptionally quiet and clean, but 

 at lower temperatures this was not better than usual. The results are 



4.i5 </ = 79. = 0.00372 



somewhat below the preceding value. 



81. Final experiments at 100. Somewhat later, at a time when the labo- 

 ratory was relatively quiet and after the same effective improvements had 

 been made in the mounting of the interferometer mirrors, the experiments 



